We carry out a systematical study of the spectral lag properties of 50 single-pulsed gamma-ray bursts (GRBs) detected by the Fermi Gamma-Ray Burst Monitor. By dividing the light curves into multiple consecutive energy channels, we provide a new measurement of the spectral lag that is independent of energy channel selections. We perform a detailed statistical study of our new measurements. We find two similar power-law energy dependencies of both the pulse arrival time and pulse width. Our new results on the power-law indices would favor the relativistic geometric effects for the origin of spectral lag. However, a complete theoretical framework that can fully account for the diverse energy dependencies of both arrival time and pulse width revealed in this work is still lacking. We also study the spectral evolution behaviors of the GRB pulses. We find that a GRB pulse with negligible spectral lag would usually have a shorter pulse duration and would appear to have a "hardness-intensity tracking" behavior, and a GRB pulse with a significant spectral lag would usually have a longer pulse duration and would appear to have a "hard-to-soft" behavior.